Hello /ic/, I am trying to work on my dogshit handwriting and

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Hello /ic/, I am trying to work on my dogshit handwriting and I was looking for any advice that you may be able to offer. I know it is best to have my pencil rest between my thumb and index knuckles, and I also know that I should write using wrist and shoulder rather than my fingers. So far I have encountered two main problems. The first and most significant is how to draw horizontal lines, should I use my shoulder to drag the pencil (which creates very poor looking lines) or should I 'squeeze' the pencil inwards? The second problem I have is how to write on a ring binder. I can't ignore this because the whole purpose of improving my handwriting is to take better notes, but when my hand comes into contact with the rings it messes with my hand's stability and posture. Any advice is appreciated.